# Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic ${\mathrm{GL}}_{n}$

Dihua Jiang; Chufeng Nien; Shaun Stevens

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 4, page 991-1007
- ISSN: 1435-9855

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topJiang, Dihua, Nien, Chufeng, and Stevens, Shaun. "Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm {GL}_n$." Journal of the European Mathematical Society 017.4 (2015): 991-1007. <http://eudml.org/doc/277611>.

@article{Jiang2015,

abstract = {The Local Converse Problem is to determine how the family of the local gamma factors $\gamma (s,\pi \times \tau ,\psi )$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi $ of $\mathrm \{GL\}_n(F)$, with $F$ a non-archimedean local field, where $\tau $ runs through all irreducible supercuspidal representations of $\mathrm \{GL\}_r(F)$ and $r$ runs through positive integers. The Jacquet conjecture asserts that it is enough to take $r=1,2,\ldots ,\left[\frac\{n\}\{2\}\right]$. Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture, we formulate a general approach to prove the Jacquet conjecture. With this approach, the Jacquet conjecture is proved under an assumption which is then verified in several cases, including the case of level zero representations.},

author = {Jiang, Dihua, Nien, Chufeng, Stevens, Shaun},

journal = {Journal of the European Mathematical Society},

keywords = {irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem; irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem},

language = {eng},

number = {4},

pages = {991-1007},

publisher = {European Mathematical Society Publishing House},

title = {Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm \{GL\}_n$},

url = {http://eudml.org/doc/277611},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Jiang, Dihua

AU - Nien, Chufeng

AU - Stevens, Shaun

TI - Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm {GL}_n$

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 4

SP - 991

EP - 1007

AB - The Local Converse Problem is to determine how the family of the local gamma factors $\gamma (s,\pi \times \tau ,\psi )$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi $ of $\mathrm {GL}_n(F)$, with $F$ a non-archimedean local field, where $\tau $ runs through all irreducible supercuspidal representations of $\mathrm {GL}_r(F)$ and $r$ runs through positive integers. The Jacquet conjecture asserts that it is enough to take $r=1,2,\ldots ,\left[\frac{n}{2}\right]$. Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture, we formulate a general approach to prove the Jacquet conjecture. With this approach, the Jacquet conjecture is proved under an assumption which is then verified in several cases, including the case of level zero representations.

LA - eng

KW - irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem; irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem

UR - http://eudml.org/doc/277611

ER -

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